Question: Solve for $x$ : $ 4|x + 5| + 6 = 2|x + 5| + 2 $
Answer: Subtract $ {2|x + 5|} $ from both sides: $ \begin{eqnarray} 4|x + 5| + 6 &=& 2|x + 5| + 2 \\ \\ { - 2|x + 5|} && { - 2|x + 5|} \\ \\ 2|x + 5| + 6 &=& 2 \end{eqnarray} $ Subtract ${6}$ from both sides: $ \begin{eqnarray} 2|x + 5| + 6 &=& 2 \\ \\ { - 6} &=& { - 6} \\ \\ 2|x + 5| &=& -4 \end{eqnarray} $ Divide both sides by ${2}$ $ \dfrac{2|x + 5|} {{2}} = \dfrac{-4} {{2}} $ Simplify: $ |x + 5| = -2$ The absolute value cannot be negative. Therefore, there is no solution.